Mr. and Mrs. Nelson are going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Nelsons, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which Mr. and Mrs. Nelson hire the design firm. Which of the following statements are true? Select all that apply. he expression 50ℎ represents the total charge for Rock the House Digital Designs. a.The expression 75ℎ represents the total charge for Elegance Home Architects.
b.The expression 500 + 75ℎ + 50ℎ represents the total amount the Nelsons will spend working drawings of their new house plans.
c.If the Nelsons hire the design firm for 15 hours, then Elegance Home Architects will be cheaper.
d.If the Nelsons hire the design firm for 25 hours, then Rock the House Digital Designs will be cheaper.

The correct statements are (a), (c) and (d).

Step-by-step explanation:

The information provided is:

Rock the House Digital Designs charges $500.00 for the initial consultation with the Nelsons plus $50.00 for every additional hour of work for the house plans.Elegant Home Architects charge $75.00 per hour for the house plans.The variable h represent the number of hours for which Mr. and Mrs. Nelson hire the design firm.

The total charge for Elegance Home Architects, if the Nelsons choose them will be:

Total for Elegance = 75 × h = 75h.

Suppose  the Nelsons hire the design firm for 15 hours.

Total for Elegance = 75 × h = 75 × 15 = $1,125

Total for Rock = 500 + (50 × h) = 500 + (50 × 15) = $1,250

So, the  Elegance Home Architects will be cheaper.

Suppose  the Nelsons hire the design firm for 25 hours.

Total for Elegance = 75 × h = 75 × 25 = $1,875

Total for Rock = 500 + (50 × h) = 500 + (50 × 25) = $1,750

So, the Rock the House Digital Designs will be cheaper.

Thus, the correct statements are (a), (c) and (d).

The average rate of change between x = 4 and x = 6 for the function

f(x) = 2x3 + 4 is 152.

Step-by-step explanation:

The average rate of change between x = 4 and x = 6 for the function

f(x) = 2x3 + 4 is determined by calculating the slope of the line that joins the points (4, f(4)) and (6, f(6)).

f(4) = 2(4)^3 + 4 = 132

f(6) = 2(6)^3 + 4 = 436

We calculate the slope of the line passing through the points;

(4, 132) and (6, 436)

slope = ( change in y) / ( change in x)

slope = ( 436 - 132) / ( 6 - 4)

slope = 152

Therefore, the average rate of change between x = 4 and x = 6 for the function f(x) = 2x3 + 4 is 152.